Theretore, if transforming metastable olivine does produce all earthquakes from 400 to 670 kilometers in depth [e.g. Burnley et al., 1991;. Kirby et al., 1991], then ...
GEOPHYSICAL RESEARCH LETTERS, VOL.18,NO.12,PAGES 2201-2204, DECEMBER 1991
WAVEFORM EFFECTS OFA METASTABLE OLIV]NETONGUE IN SUBDUCTING SLABS JohnE. Vidale
UnitedStates Geological Survey, MenloPark,California Quen.finWilliamsandHeidi Houstoi•
Earth Sciences Dept. andInstitute ofTectonics, University ofCalifornia, Santa Cruz Abstract.We constructed velocitymodelsof subducting slaD would differ t¾om those produced bysimple elevation of slabs with a kinetically•depressed olivine--> [3-and¾-spinel the phaseb9undary[e.g., Goto et al., 1987]. Thus, the transition,and examined the effect that suchstructureswould presence or absence of MOTO hasimportantimplications for haveon teleseismicP waveformsusinga full-wavefiniteslabstructure, thedynamics of thesubruction process, andthe difference method. These two-dimensional calculations physicalmechanism by which deepearthquakes occur. yieldedwaveformsat a rangeof distances in thedowndip Nevertheless, thepresentworkis thefirsteftbrtto examinethe direction.The slab modelsincludeda wedge-shaped, lowpossibleteleseismicsignatureof roetastable olivine within velocitymetastable olivinetongue(MOTO) to a depthof 670 subductingslabs.
kin,aswell as a plausiblethermalanomaly;onemodelfurther includeda 10-km-thickfast layer on the surfaceof the slab. SlabVelocityModel Theprincipaleffectof MOTO isto produce grazingreflections atwideanglesoff the phaseboundary, generating a secondary The generalslabvelocitystructure for whichwe compute arrival0 to 4 seconds aftertheinitialarrivaldepending on the waveforms is shownin Figure1. We assumed a slabdipof take-offangle. The amplitudeandtimingof thisfeaturevary 50%andtookthedimensions of MOTO asapproximately with the lateral location of the seismic source within the slab
equivalentto thosedefinedby the900øCslabisothermin th6 calculations of Schubert etal. [1975](ignoring thelatentheat of transformation producedby phasetransitions).This
cross-section. Careful analysis of waveforms from earthquakes with depthsnear 400 kin, simplesources,and adequatestati6n coveragein appropriategeometrieswill be required to resolvewhetherMOTO is present.
isotherm corresponds to thekineticestimate of Sung[1979] for the minimum transition temperature from (Mgo.9Feo.•)2SiO4-olivine tospinelwithintheslab,assuming
Introduction
an activation volume for the transition of z 10 cm3/mole. The
kineticsof thetransition to theB-phase arelikelyto beeither TheEarth'smantleundergoes a majorseismic and similarto, orlessrapidthanthoseto they-phase[Rubieand mineralogicchangeat about400 km depthassilicateolivine Brearley,1991]. Moreover, thisisotherm spansthedepth transformsto the higher-pressure[3-phase.This paperis concernedwith this discontinuity as it occurs in cold subducting slabs. Althoughcoldertemperatures withinslabs
arethoughtto elevatetheequilibrium boundary of theolivine to13-phase transitiondue to the positiveClapeyronslopeof thisreaction[Solomonand U, 1975; Roecker,1985;Helffrich et al., 1989], low temperaturescould insteadkinetically impedethereaction,thusdepressing thisboundary withinthe
range over which deep earthquakesoccur. Theretore, if
transforming metastable olivinedoesproduce all earthquakes from400to 670kilometers in depth[e.g.Burnleyetal., 1991; Kirbyet al., 1991],thena low-velocityfeaturewithaboutthe lengthshownin FigureI mustbepresent withintheslab. We assume a 5% contrast in P-wavevelocityacrossthe phaseboundarywithin the slab. This corresponds to an olivine abundanceof about 60% within the slab at 400 km
coreof theslab[Sung,1979;SungandBums,1976]. Thus, depth, andisconsistent withestimates of theP-wave velocity a wedge-shaped regionof roetastable olivinemaypersistin subducted lithosphere to depthswell below400 kin. Sucha feature wouldforma relatively. low-velocity andlow-density Modelof metastable olivinetongue channel withinthe slabthatwouldactasa seismicwaveguide. (MOTO) in subductingslab Thislow-velocitystructuremightbe difficultto observeby : 7::. i::• :s..•..: arrivaltimetomography, sincethefirstarrivingseismicwaves '•, .....•---'-.•:. oliVifie. tendto stayin fast material[Iidaka and Suegetsu, 1990]. Here,we investigate the effectson teleseismically-recorded sot/rces'X•, compressional (P) waveformsof a roetastable olivinetongue ",. x',x... 'X? [3-phase (MOTO) extendingfrom 400 km to 670 km in orderto ', ' ", + ?spinel evaluatethe prospectsfor resolvingthe presenceof sucha structure.
The geophysicalconsequences of sucha featureare profound.It hasbeensuggested thatdeepearthquakes are caused by a shearinstabilityassociated withthetransformation
of roetastable olivineto its high-pressure phases (•, witha spinelloid structure and¾,withthespinelstructure) in theslab underdeviatoricstresses [Burnleyet al., 1991;Kirby et al., 1991;Greenet al., 1991]. Furthermore, if MOTO is present,
thenboththebuoyancy forcesandthestress statein thedeep
Copyright 1991 bytheAmerican Geophysical Union.
670km ,,
pv + mw
Fig. 1. Schematic of slabmodelwith low-velocitymetastable
olivinetongue(MOTO)withinthesubducting slab. Velocity contrastacrosstheolivine--> It-phase + ¾-spinel boundaryis assumed to be 5%; thewidthof thelow-velocitywedgeis 70 km at 400 km depth. Starsshow different sourcelocations usedto computewaveforms. Approximatelocationsof the
equilibrium phasetransitions t¾omolivineto theIt-phase, and from¾-spinel to perovskite andmagnesiowtistite (pv+mw)are
Papernumber91GL02588
shownby dottedlines. Dashedlines indicatethe extentof the slabthermalanomaly.
0094-8534/91/91GL-025 88503.00 2201
2202
Vidaleet al.: WaveformEffectsof a Metastable OlivineTonguein Subducting Slabs Take-off
contrastacrossthe 400 km discontinuity in ambientmantle
angle
[LeFevre andHelmberger, 1989].Thevelocitydiscontinuity acrossthetransitionis assumed to besharp:Sung[1979]has estimated thatthistransition will proceed from 10 to 90% completion across abouta 50øCinterval in temperature. In the
. I I I *.. I...... I I
. I t I Distance
17 ø
25 ø
slabthermalmodelof Schubertetal. [1975],thiscorresponds to a thickness of the transition of less than ~7 kilometers.
Thus,relativeto its overalldimension andthewavelengths of the seismicwaves,the boundariesof the featureare likely to
85 ø
33 ø
67 ø
40 ø
50 ø
48 ø
33 ø
be relativelysharp. However,we notethepossibility that
regionsof metastable olivinemay be heterogeneously distributed in thesubducting slab,withnon-planar boundaries between theo!ivineandspinelphases [Frohlich,1987]. Our model also includes an elevation of the olivine to •-
....
0
2
4
6
0
2
4
6
0
2
4
6
8
Fig.2. Teleseismic P waveforms froma sourceat location! (seeFigure 1) for slabmodelsincluding:(a) only a thermal anomalyof 3.5%, (b) the thermalanomalyand the MOTO
phase transition in thehighertemperature, non-kineticallystructure asshownin Figure1, and(c) thethermalanomaly, impeded regions of theslabby approximately 25kilometers. the MOTO structure,and a high-velocity(5% fast) 10-kmThisis based upona Clapeyron slopeforthistransition of thicklayeronthesurfaceof theslab. -1.5 x 10-3 GPa/øC[Akaogietal., 1989],andan assumed
temperature difference between thekinetic boundary andthe ambientmantleof-500øC at 400 kilometersdepth[Sung,
1979;Helffrichetal., 1989;Akaogietal., !989]. The670 km depthdiscontinuity mayalsobe displaced dueto the
thermalanomalyassociated with the slab,butthisfeature wouldnot producea significant effecton the calculated waveformsandis not includedin ourvelocitymodels.
All ourmodelsincorporate thelongerwavelength thermal
perturbation invelocity structure thought tobeassociated with the slab. Specifically, we assume -0.4 m/sec/øC for the derivativeof the compressional velocity with respectto
temperature (dVp/dT)[e.g.Anderson, !987]. Wealso
affectedby MOTO, becausethe seismicwavescantravelthe entirelengthof thestructure.As expected, simulations witha sourceat 580 km depthshowedmuchlesseffectof theMOTO structureon waveforms than those with sourcesnear 400 km.
Figure2 is a comparisonof waveformsgeneratedby differentslabstructures with a sourceat 400 km depthnearthe
uppersurface of theslab(location1 in Figure1). Theprimary effectof thethermalanomaly(Figure2a) is to broaden and reducetheamplitudeof thewaveforms for take-offanglesnear thedip of theslab(at distances between500 and750tbr a slab dipping50ø);seeVidale [1987] for furtherdiscussion of the
assumea maximumtemperature changeof approximately effect of variousthermal anomalieson w&veforms.When the 800øC, with a width of 200 km basedon the estimated MOTO structureis included(Figure2b), the effect of the locationsof isothermswithin the slab[Schubertetal., 1975;
Helffrichetal., 1989]. The resulting velocityanomaly is 3.5% fastnearthe uppersurfaceof theslab,anddropsoff linearlyto 0% anomalyboth30 km normalto theslababove and 170 km below the maximumvelocity(e.g., the coldcore of the slab). All modelsalsoincludethe normalincreases of seismicvelocitywith depth. The final structural element testedin our simulationsis a 10-
km-thicklayeron theuppersurfaceof theslabwitha velocity 5% higherthanambientmantle;weextend thislayertoa depth of 1000 km. Such a structurehas beeninv.okedto explain earlyarrivalsin New Zealandfromeventsin Tonga[Arisell and Gubbins, !986].
thermalstructure is partiallycounteracted. More significantly,however, the presenceof MOTO
introduces grazingreflectionsat wide anglesoff the sharp phaseboundary. Dependingon the take-off angle,these reflections cangenesrate a secondary arrival0 to 3 seconds after thefrrstarrival. The strongsecondary arrivalat shallowtakeoff anglesin Figure2b is thereflectionoff theloweredgeof MOTO. At steeptake-offangles,thesecondary arrivalis nota geometricray, but a diffraction. The first arrival consistsof energythathastraveleda shorterdistancein the low-velocity metastable olivine than later arrivals. The MOTO
structure has
an effect intermediatebetweena lens and a waveguide,
channeling •tnddelaying someof theenergy.Because the
widthof thethermalanomalyis largerelativeto thatof MOTO, Results the secondary arrivalsproducedby MOTO are not strongly affectedby the amplitudeof thethermalanomaly.Similarly, becauseof its smalllengthscale,theeffectof a 10-kin-thick, Compressional waveformswerecomputed usingthetwodimensional, fourth-order finite difference method of Vidale fastlid nearthe uppersurfaceof theslabis notlarge(Figure [1990] with an isotropic source. The full-wave finite 2c). This structureaccentuates thesmallsecondary arrivalat anddepletes difference scheme isusedto propagate seismic wavesthrough take-offanglesbelowtheslab(largedistances), at take-offanglesabovethe slab(small theslabmodel;a Kirchhoff method isthenusedtoextrapolate the highfrequencies
thewavesto teleseismic distances [SteadandHelmberger, distances). Results of simulationsincluding the simplestMOTO 1988]. The two-dimensional simulations yieldan accurate
approximation in thedowndipdirection.Conversions of shear to compressional wavesare ignoredin our acousticwave
simulations; theinclusion of suchconversions wouldmainly serveto furthercomplicate thelaterpartofthewaveform. Waveformswere computedfor take-off anglesat
approximately 4øincrements aboveandbelowthedipof the slab. Fora slabthatdips50ø(recallthatdipismeasured from thehorizontalandtake-offanglefromthevertical),take-off anglesfrom50ø to 20øspanthedistance rangeof 30øto 90ø. This geometry resemblespaths from the Kurile slab to
Europeanstations.Subduction zonesthatdip moreor less than 50o will show a similarpatternof waveformeffects shiftedtogreater orsmaller distances, respectively. Seismicsources areplacedat depths near400km, asthisis
structureand the thermalanomaly,with sourceslocatedat points1, 2, and3 in Figure1, areshownin Figures3a,b, and c, respectively. All three sourcesgive rise to secondary arrivalsproducedby grazingreflections off the olivine-spinel boundary. The amplitudeand timing of thesesecondary arrivalsdependon thelaterallocationof thesourcewithinthe slabcross-section, as well as the take-offangle. This strong dependence of the waveforms on source location will
introducesomeuncertainty into theinterpretation of actual waveforms, as thepreciselocations of deepearthquakes are presentlypoorlyknown.
if theolivine--> [1-orT-spineltransitions havepositive activation volumes, thenat greaterdepths, thetemperature at which the transformation occurs in the slab would increase
thesource depthat whichwaveforms will bemoststrongly [Sung, 1979]. Thus, the boundariesof MOTO may be
Vidale etal.' Waveform Effects ofaMetastab!e Olivine Tongue inSubducting Slabs (a) Source 1
(b) Source2
amount of broadband teleseismic
(c) Source3
Take-off
angle • •
•
• ....... I •
33ø•./-"•----••
•
400
-
•
•
• ......... •
•..•----..•.•_....• .
- 2.._.--...'•, .
67ø ' 50"
.
0
2
4
6
0
2
4
6
0
2
4
6
8
Seconds
Fig.3. Teleseismic P waveforms fromsources at different
broaderthan a given isothermat depth within the slab, increasing theregionof olivinemetastability, andproducing a broader,blunter structure than is shown in Figure 1.
in an
appropriate geometrywithsufficientlydensestationcoverage. However,noneof theseproblemsprecludeusingteleseismic waveforms toresolvewhetherMOTO is present. ff roetastable olivineexistswithintheslab,it may be present in structures morecomplex thanthesimplestructures modeled here. Suchstructuresmight have irregularboundariesor regions convertedto spinel distributedheterogeneously throughout thewedge[e.g.FrohIich,1987]. The effectsof a morecomplicated structure aredifficultto predict.We expect thatgreaterstructural complexitywith scalelengthsof 5 to 50 km wouldproducemorewaveformcomplexity;however,it may also depletehigherfrequencies.Increasedwaveform complexity may facilitate the identification of metastable olivine,whereas depletion of higherfrequencies mayhinderit.
locationsin a slab with the MOTO structure.The sourcesfor
(a), (b), and (c) are at points !, 2, and 3, respectively, in Figure1.
data collected
2203
Conclusions
Thisstudyprovidesonemeansby whichthepresence of a low-velocitymetastableolivine wedgewithin a subducting slabcouldbeseismically resolved.Althoughthedetailsof the waveformsdependon sourcelocation within the slab, our simulations document that MOTO
structures similar to those
modeledherewill generatesignificantwaveformcomplexity, arrivals0 to 4 seconds after Simulationswith a slab model incorporatinga broadened, primarilyin theformof secondary theinitialP wavefor eventsnear400 km depth.Teleseismic roundedMOTO indicate that the effect on waveforms is not significantly different fromthatof a wedge-shaped structure. waveformsrepresenta promisingmechanismwith whichto Takentogether,our simulations document thata structure examinesucha feature,althoughsomedifficultiesmayarisein similar to MOTO will produce prominent waveform practice. These include uncertainty in sourcelocation, a
near400km depth,earthquake source complexity in theformof secondary arrivals atsometake-off paucityof earthquakes angles regardless of the locationof a 400 km deepsource complexity, limited broadbandteleseismic data with the withintheslab. Thiscomplexity is present for all thevelocity appropriategeometry, and interference from core-related phases. structures thatwe testedandfor variousamplitudes of theslab thermalanomaly. Shearwaveformsmayexhibitsomewhat
greater complexity thancompressional waveforms; however, sinceshear waves are more attenuated,the complications wouldprobablybemoredifficultto resolve. Some effects of the MOTO structureon the waveformscan
befairlysubtle; forexample, risetimes(thetimefrominitial arrival to peakamplitude) of P-waveforms ofevents near400 kmdepthareeitherunchanged or lengthened by MOTO. Therefore, observations of deep(>450km) earthquakes with
Acknowledgements: We thank T. Lay, E. Knittie, S. Grand, S. Kirby, and H. Benz for helpful comments. Contribution#140 of the Institute of Tectonics (C.F. Richter
Seismological andMineralPhysicsLaboratories).This work was partially supportedby NASA (Q.W.), NSF (H.H.) and the W.M.
Keck Foundation.
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